(Tentative) Office hours M 2-3, F 11-12 in MATH 303.

Syllabus for course

Text: W. Trappe and L. Washington, An Introduction to Cryptography with Coding Theory, Second Edition. (Prentice-Hall)

Date | Section and Topic | Read before class | Homework |

August 28 | Organization and introduction | Section 1.1 | HW 1 due Sept 6 |

August 30 | Cryptosystems and applications | Section 1.2 | Start of HW 1, click here |

Sept 1 | Shift and affine ciphers | Sections 2.1, 2.2 | HW 1 (cont.) p55, 1-6 (grad students also do 7) |

Sept 6 | Vigenere Codes | Section 2.3 | HW 2 due Sept 13 |

Sept 8 | Block ciphers, ASCII, one-time pads | Sections 2.7-2.9 | p55, 10, 13, 14, 15, 17, 18 (grad students also do 11, and prove that a (square) matrix with integer entries is invertible module n if and only if its determinant is invertible mod n.) |

Sept 11 | Divisors, primes, and GCDs | Section 3.1 | HW 3: Due Sept 20 |

Sept 13 | Back substitution, unique factorization | Section 3.2 | p 104, 1, 3, 4, 5, 6, 7, 8 (grad students prove there are infinitely-many primes congruent to 5 mod 6.) |

September 15 | Infinitude of primes, integers mod n | Section 3.3 | |

September 18 | Division mod n, CRT | Section 3.4 | HW 4 due Sept 27 |

September 20 | Modular exponentiation: Fermat and Euler | Sections 3.5, 3.6 | 105, 10, 13, 15, 16, 17, 20, 21, 26 (grad students, also 22, 39) |

September 22 | Phi function, Primitive roots | Sections 3.7-3.9 | |

September 25 | Inverting matrices mod n, Square roots mod n, Quadratic Residues | Sect 3.10 | Exam 1, Sept. 29 |

September 27 | Review for Exam I | Sect 1.1-1.2, 2.1-2.4, 2.7-2.9, 3.1-3.8 | |

September 29 | Exam I | Have a good weekend | |

October 2 | RSA | Sect 6.1 | HW 5 due Oct 11 |

October 4 | Attacks on RSA | Sect 6.2 | p. 192, 1, 2 a, 5, 6, 7, 9, 10, 15. Grad students do 23. |

October 6 | Primality testing: Miller-Rabin | Sect 6.3 | |

October 9 | Primality testing: Solovay-Strassen | Sect 6.3 | HW 6 due October 18 |

October 11 | Factoring | Sect 6.4 | HW #6: p 192, 12, 13, 28. Use the Miller-Rabin test to show that 49 is composite. Use the Solovay-Strassen test to show 49 is composite. Use Pollard method to factor 49. |

October 13 | Discrete logarithms, Diffie-hellman key exchange | Sect 7.1, 7.4 | |

October 16 | Pohlig-Hellman | Sect 7.2 | |

October 18 | ElGamal Cryptosystem | Sect 7.5 | |

October 20 | RSA digital signatures | Sect 9.1 | HW 7 due Oct 25: p 252, 1, 2, 4, 6, Grad students do 8 |

October 23 | ElGamal digital signatures | Sect 9.2 | |

October 25 | Intro to Probability | Sect 15.1 | HW 8 due Nov 1: p 343, 1, 2, 3, 4, Grad students due 6a |

October 27 | Randon variables, entropy | Sect 15.2 | |

October 30 | Joint and condition entropy: information | Sections 15.2 | |

November 1 | Answer questions about test | Sections 3.10, 6.1-6.4, 7.1 , 7.2, 7.4, 7.5, 9.1, 9.2, 15.1, 15.2 | |

November 3 | Exam 2 | Have a good weekend! | |

November 6 | Prefect security of the 1-time pad | ||

November 8 | Introduction to coding | Sect 18.1 | |

November 10 | Hamming metric, rate, Shannon's coding theorem | Sect 18.2 | HW 9 due Nov 15: Test corrections plus p 445, 1, 2, 5, 7, 15. |

November 13 | Bounds on codes | Sect 18.3 | |

November 15 | Gilbert-Varshamov bound; intro to finite fields | Sect 18.3, 3.11 | HW 10 due Dec. 1: p 110, 33, 34; p. 446, 3, 6, 8. For the grad students: for which primes p is x^2+x+1 irreducible mod p? |

November 17 | Construction of finite fields | Sect 3.11 | Have a good break! |

November 27 | Intro to Linear Codes | 18.4 | |

November 29 | Generating Matrices and Check Matrices | 18.4 | |

December 1 | Dual Codes and Syndromes | 18.4 | HW 11 due Dec 6: Chpt 18; 4, 9, 10, Grad students 16. |

December 4 | Cosets, Hamming codes | 18.5 | |

December 6 | Cyclic Codes | 18.7 | Take home final due 4pm on Dec 18 |

December 8 | Cyclic codes, BCH bound | 18.7, p. 433 | |

December 11 | Reed-Soloman codes | 18.9 | |

December 13 | McEliece Cryptosystem | 18.10 |